Probability on Trees and Networks

This is close to the final version that will be published by Cambridge University Press. An online version will always remain free. You can order a hard copy of the book here.

Please let us know of any errors you find; send them to rdlyons@indiana.edu or peres@microsoft.com.

You may wish to use the following if you refer to this book in a paper.

@book{LP:book,
author = {Russell Lyons and Yuval Peres},
title = {Probability on Trees and Networks},
publisher = {Cambridge University Press},
address = {New York},
pages = {xvi+699},
year = 2016,
note = {Available at \url{http://pages.iu.edu/~rdlyons/}},
}

In the electronic version of this book, most symbols that are used with a fixed meaning are hyperlinked to their definitions, although the fact that such hyperlinks exist is not made visible.

Because of current technology, color is used slightly differently in the electronic and printed versions.

Chapter Titles:

Some Highlights
Random Walks and Electric Networks
Special Networks
Uniform Spanning Trees
Branching Processes, Second Moments, and Percolation
Isoperimetric Inequalities
Percolation on Transitive Graphs
The Mass-Transport Principle and Percolation
Infinite Electrical Networks and Dirichlet Functions
Uniform Spanning Forests
Minimal Spanning Forests
Limit Theorems for Galton-Watson Processes
Escape Rate of Random Walks and Embeddings
Random Walks on Groups and Poisson Boundaries
Hausdorff Dimension
Capacity and Stochastic Processes
Random Walks on Galton-Watson Trees
Comments on Exercises
Bibliography
Glossary of Notation
Index